Solve (2/sqrt{4}-1/3(4^3)+4^2)-(2/-4-1/3(-4^3)+(-4^2)

$$( \frac{ 2 }{ \sqrt{ 4 } } - \frac{ 1 }{ 3 } ( { 4 }^{ 3 } )+ { 4 }^{ 2 } )-( \frac{ 2 }{ -4 } - \frac{ 1 }{ 3 } ( { -4 }^{ 3 } )+(- { 4 }^{ 2 } )$$

Evaluate

$$-\frac{55}{6}\approx -9.166666667$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2}{2}-\frac{1}{3}\times 4^{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Divide 2 by 2 to get 1.

$$1-\frac{1}{3}\times 4^{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Calculate 4 to the power of 3 and get 64.

$$1-\frac{1}{3}\times 64+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Multiply \frac{1}{3} and 64 to get \frac{64}{3}.

$$1-\frac{64}{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{64}{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Since \frac{3}{3} and \frac{64}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-64}{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Subtract 64 from 3 to get -61.

$$-\frac{61}{3}+4^{2}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{61}{3}+16-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Convert 16 to fraction \frac{48}{3}.

$$-\frac{61}{3}+\frac{48}{3}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Since -\frac{61}{3} and \frac{48}{3} have the same denominator, add them by adding their numerators.

$$\frac{-61+48}{3}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Add -61 and 48 to get -13.

$$-\frac{13}{3}-\left(\frac{2}{-4}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{3}-\left(-\frac{1}{2}-\frac{1}{3}\left(-4\right)^{3}-4^{2}\right)$$

Calculate -4 to the power of 3 and get -64.

$$-\frac{13}{3}-\left(-\frac{1}{2}-\frac{1}{3}\left(-64\right)-4^{2}\right)$$

Multiply \frac{1}{3} and -64 to get \frac{-64}{3}.

$$-\frac{13}{3}-\left(-\frac{1}{2}-\frac{-64}{3}-4^{2}\right)$$

Fraction \frac{-64}{3} can be rewritten as -\frac{64}{3} by extracting the negative sign.

$$-\frac{13}{3}-\left(-\frac{1}{2}-\left(-\frac{64}{3}\right)-4^{2}\right)$$

The opposite of -\frac{64}{3} is \frac{64}{3}.

$$-\frac{13}{3}-\left(-\frac{1}{2}+\frac{64}{3}-4^{2}\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{64}{3} to fractions with denominator 6.

$$-\frac{13}{3}-\left(-\frac{3}{6}+\frac{128}{6}-4^{2}\right)$$

Since -\frac{3}{6} and \frac{128}{6} have the same denominator, add them by adding their numerators.

$$-\frac{13}{3}-\left(\frac{-3+128}{6}-4^{2}\right)$$

Add -3 and 128 to get 125.

$$-\frac{13}{3}-\left(\frac{125}{6}-4^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{13}{3}-\left(\frac{125}{6}-16\right)$$

Convert 16 to fraction \frac{96}{6}.

$$-\frac{13}{3}-\left(\frac{125}{6}-\frac{96}{6}\right)$$

Since \frac{125}{6} and \frac{96}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{3}-\frac{125-96}{6}$$

Subtract 96 from 125 to get 29.

$$-\frac{13}{3}-\frac{29}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{13}{3} and \frac{29}{6} to fractions with denominator 6.

$$-\frac{26}{6}-\frac{29}{6}$$

Since -\frac{26}{6} and \frac{29}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26-29}{6}$$

Subtract 29 from -26 to get -55.

$$-\frac{55}{6}$$

Factor

$$-\frac{55}{6} = -9\frac{1}{6} = -9.166666666666666$$